Can a 4” APO ‘beat’ an 8” SCT? (yes and no)

Can a 4” APO ‘beat’ an 8” SCT? (yes and no)
by Gary S. Strumolo

This article is derived from a talk I gave my local astronomy club many years ago. This competition, and variations of it using different types and sizes of telescopes, seems to be a perennial question. Our goal in writing it was not to disparage any type of scope; all have their use and, like beauty, their value to an individual is in the eye of the beholder. We’ll not bring up issues like portability, weight, cool-down time, cost, or any of the many other factors that go into a purchase decision.

Rather, we’ll focus on the optics and their ability to render visually appealing images of both low and high contrast objects. We are not going to address what could be generated after recording, stacking, and processing thousands of video images. This analysis is not for astrophotographers; it’s for visual astronomers!

The tool we’ll use to conduct this analysis is called the modulation transfer function, or MTF for short. The MTF curve for an optical system, like a telescope, determines how much contrast of the object being observed is maintained after passing through the optical system. It can be illustrated here:

The MTF curve reflects the ratio of image contrast to object contrast.(This and all subsequent MTF curves were generated by the Windows program Aberrator).The type of curve above is typical for an unobstructed scope, like a refractor. If you compare two refractors of different apertures you get:

basically showing that the larger scope can reveal finer details on the object than the smaller one can. Aberrator can analyze more than an unobstructed lens, however:

In this example, we consider the case of an 8” aperture with a 33% central obstruction, as found in your typical 8” SCT. The downward bend in the curve reflects the fact that low contrast resolution is degraded because of the obstruction. To determine how much we consider the previous graph and ask how much smaller in diameter must the aperture be so that the new (unobstructed) curve will line up with this dropped down portion. That will give us the ‘effective’ size of an unobstructed scope that will match this one for low contrast features.

For example, consider this for an obstructed scope:

The black ideal curve is for an unobstructed aperture (refractor). The red actual behavior curve is for an obstructed aperture of the same size. The low contrast blue line, which matches the red curve drop, is for a smaller unobstructed scope. To determine its size we look to see where the blue curve hits the X-axis. Here it is around 0.7, which means the original scope performs like an unobstructed one 70% of it’s diameter.

The effects of a central obstruction on the ability to resolve low contrast features can be illustrated in the following diagram (20% for a typical Newtonian and 33% for a typical SCT):

So, e.g., the 20% obstructed scope (blue line) behaves like an unobstructed one 85% of its diameter (blue dashed line). Now obstruction isn’t the only factor in making the final decision about which is better. There are two others: collimation and seeing (turbulence). Let’s consider each, and how they are linked to the obstruction issue.

Collimation (for more, see T. Legault astrophoto.fr/collim)

Most people are familiar with the first phase of collimation, where you pick a star and deliberately rack it out of focus. You will see a set of rings (if you have an obstructed scope like a Newtonian, SCT or MCT there will be a dark central circle in the middle). The goal of ‘rough’ collimation is to make everything perfectly concentric. But that isn’t the end!

(and the bane of MCTs and Newtonians as well). The second stage is to use high powers on a focused star to see the Airy disks. These must also be concentric. As the figure above indicates, fig A is ideal while Fig D is still off. Now, how bad is it? Well, consider the pattern in Fig C above. It doesn’t look that bad, right? Well …

The figure above is an example for a Newtonian. We can see that that a C level of miscollimation produces an MTF curve that is similar to one from a spherical aberration of 1/3.5 wave, and one with a 43% obstruction. These are ‘equivalent’ to a 20% obstructed scope at 63% diameter (again, for resolving low contrast features).

So returning to our SCT:

we can see that while a perfectly collimated 8” SCT under excellent seeing conditions might behave like a 5.6” APO (left), poor collimation can reduce it to the level of of a 4” APO or worse! (hence the ‘yes and no’ in the title)

Seeing conditions (turbulence)

We will equate seeing conditions to turbulence in the atmosphere, ignoring things like poor transparency due to clouds, etc.. Now different aperture scopes are affected differently by turbulence:

(source: https://skyandtelescope.org/astronomy-equipment/beating-the-seeing/)

This behavior might actually help the smaller scope over the larger one during visual astronomy because the eye can better follow detail as it moves a bit vs being steady but blurry. And unless you live in areas blessed with frequent steady skies …

But given the observation above, the effective turbulence for a larger scope is greater than that for a smaller scope. So we could be in the following situation:

So under fair-below average seeing conditions (which many people deal with most of the time) it’s possible for a reasonably well collimated 8” SCT to simply match a 4” APO.

So how do these analysis results compare to observations?

l  An 8” beats a 4” on high-contrast objects (moon craters, Cassini division, shadow transits, edge of planet)

l  A 4” can match (or possibly beat) an 8” on low-contrast objects (surface of Jupiter and Saturn, possibly Mars) except under very good-excellent seeing conditions.

To test this, we can use the Aberrator program to simulate the effects of turbulence on image quality:

We can see that under no turbulence the SCT beats the APO even for the low-contrast surface features of Jupiter, but when there is turbulence the image quality is equal.

I hope this helps explain the factors behind the quality of what you see in the EP. Of course, size matters, and if your goal is DSOs then the larger scope will always win out (after all, they are called ‘faint fuzzies’ for a reason). But, as we all know, the ‘best’ telescope is the one we use the most!

Thanks for reading and clear skies!

Gary S. Strumolo